An oil supply apparatus includes an oil pump that is driven by an internal combustion engine; a supply passage that is connected to a discharge side of the oil pump; a lubricant passage that leads hydraulic fluid from the supply passage to a portion to be lubricated that is provided in the internal combustion engine; a hydraulic passage that leads hydraulic fluid from the supply passage to a variable valve mechanism; a flow regulating valve capable of regulating a flowrate of hydraulic fluid that flows through the lubricant passage; and a control apparatus that controls the flow regulating valve in a closing direction at startup of the internal combustion engine such that a pressure of hydraulic fluid that is led to the variable valve mechanism when the internal combustion engine is being cranked comes to be equal to or greater than a predetermined target pressure.